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We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to any other stable distance. In contrast, via a specific construction, we show that the interleaving distance and the functional distortion distance on Reeb graphs are not universal., Author(s): Ulrich Bauer [sup.1] , Claudia Landi [sup.2] , Facundo Mémoli [sup.3] Author Affiliations: (1) grid.6936.a, 0000000123222966, Department of Mathematics, Technical University of Munich (TUM), , Munich, Germany (2) grid.7548.e, [...]

In this paper, we obtained the analytical N-dimensional bound state solutions of exponential-type potential functions using the semi-classical Wentzel-Kramers-Brillouin (WKB) approximation method with an improved approximation to the orbital centrifugal barrier. Furthermore, we derived the partition function with the associated thermodynamic properties. We calculated the expectation values () via the Hellmann-Feynman theorem. Our results for the energy levels are in excellent agreement with the best available results obtained by other methods in the existing literature. The variations of the thermodynamic functions with the temperature parameter ([beta]) agree very well with the other results obtained under different potential energy functions. The expectation values conformed to the ones obtained by another approach in previous work. This work demonstrates the exactness of the leading-order WKB approximation. Key words: Manning-Rosen potential, Eckart potential, Hulthen potential, thermodynamic properties, WKB approximation method. Nous obtenons ici les solutions analytiques a N-dimensions des etats lies de potentiels de type exponentiel, en utilisant la methode de l'approximation semi-classique WKB avec une approximation amelioree pour la barriere centrifuge orbitale. Ensuite, nous derivons la fonction de partition avec ses fonctions thermodynamiques associees. Nous calculons les valeurs moyennes () via le theoreme de Hellmann-Feynman. Nos resultats pour les niveaux d'energie sont en excellent accord avec les meilleurs resultats obtenus d'autres methodes retrouves dans la litterature. Les variations des fonctions thermodynamiques avec le parametre de la temperature ([beta]) sont en tres bon accord avec les autres resultats obtenus pour differentes fonctions d'energie potentielle. Les valeurs moyennes obtenues sont conformes a celles obtenues par d'autres approches dans des travaux anterieurs. Ce travail demontre l'exactitude de l'approximation WKB au premier ordre. [Traduit par la Redaction] Mots-cles : potentiel de Manning-Rosen, potentiel d'Eckart, potentiel de Hulthen, proprietes thermodynamiques, methode de l'approximation WKB., 1. Introduction In quantum mechanics and applied physics, the solutions to the wave equations play an important role in understanding the properties of physical systems. Of these properties, the eigen-solutions [...]

MacMahon's Partition Analysis (MPA) is a combinatorial tool used in partition analysis to describe the solutions of a linear diophantine system. We show that MPA is useful in the context of weighted voting games. We introduce a new generalized generating function that gives, as special cases, extensions of the generating functions of the Banzhaf, Shapley-Shubik, Banzhaf-Owen, symmetric coalitional Banzhaf, and Owen power indices. Our extensions involve any coalition formation related to a linear diophantine system and multiple voting games. In addition, we show that a combination of ideas from MPA and Clifford algebras is useful in constructing generating functions for coalition configuration power indices. Finally, a brief account on how to design voting systems via MPA is advanced. More precisely, we obtain new generating functions that give, for fixed coalitions, all the distribution of weights of the players of the voting game such that a given player swings or not. Finding: This work was supported by Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq-Brazil) under [Grant 307211/2015-0]. Keywords: Banzhaf power index * Shapley-Shubik power index * coalitional power indices * coalition configuration * generating functions * linear diophantine system * Omega Calculus * Clifford algebra * weighted voting games * design of voting systems, 1. Introduction Power indices for weighted voting games (WVGs) have been a subject of recurrent interest (see, e.g., Felsenthal and Machover [25], Holler and Nurmi [33]). Two of the main [...]

We consider a nonatomic selfish routing model with independent stochastic travel times for each edge, represented by mean and variance latency functions that depend on edge flows. This model can apply to traffic in the Internet or in a road network. Variability negatively impacts packets or drivers by introducing jitter in transmission delays, which lowers quality of streaming audio or video, or by making it more difficult to predict the arrival time at destination. At equilibrium, agents may select paths that do not minimize the expected latency so as to obtain lower variability. A social planner, who is likely to be more risk neutral than agents because it operates at a longer time scale, quantifies social cost with the total expected delay along routes. From that perspective, agents may make suboptimal decisions that degrade long-term quality. We define the price of risk aversion (PRA) as the worst-case ratio of the social cost at a risk-averse Wardrop equilibrium to that where agents are risk neutral. This inefficiency metric captures the degradation of system performance caused by variability and risk aversion. For networks with general delay functions and a single source--sink pair, we first show upper bounds for the PRA that depend linearly on the agents' risk tolerance and on the degree of variability present in the network. We call these bounds structural, as they depend on the structure of the network. To get this result, we rely on a combinatorial proof that employs alternating paths that are reminiscent of those used in max-flow algorithms. For series-parallel graphs, the PRA becomes independent of the network topology and its size. Next, we provide tight and asymptotically tight lower bounds on the PRA by showing a family of structural lower bounds, which grow linearly with the number of nodes in the graph and players' risk aversion. These are tight for graph sizes that are powers of 2. After that, by focusing on restricting the set of allowable mean latency and variance functions, we derive functional bounds on the PRA that are asymptotically tight and depend on the allowed latency functions but not on the topology. The functional bounds match the price-of-anarchy bounds for congestion games multiplied by an extra factor that accounts for risk aversion. Finally, we turn to the mean-standard deviation user objective--a much more complex model of risk aversion because the cost of a path is nonadditive over edge costs--and provide tight bounds for instances that admit alternating paths with one or two forward subpaths. Funding: Part of this work was done while the first two authors were visiting the Simons Institute for the Theory of Computing at Berkeley and the third author had a faculty position at Universidad Torcuato Di Telia in Buenos Aires, Argentina. This research was supported by National Science Foundation [Grants CCF-1216103, CCF-1350823, and CCF-1331863], National Scientific and Technical Research Council (CON1CET), Argentina [Grant PIP 112-201201-00450CO], and Agenda Nacional de Promocion Cientifica y Tecnologica (ANPCyT), Argentina [Grant PICT-2012-1324]. Keywords: stochastic Wardrop game * risk aversion * price of anarchy, 1. Introduction A central question in decision making is how to make good decisions under uncertainty, particularly when decision makers are risk averse. Applications of crucial national importance, including alleviating [...]

We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of decay of the probability that the sample path of the evolutionary process lies in a prespecified set as the population size approaches infinity. We use these results to describe excursion rates and stationary distribution asymptotics in settings where the mean dynamic admits a globally attracting state, and we compute these rates explicitly for the case of logit choice in potential games. Funding: Financial support from the National Science Foundation [Grants SES-1155135, SES-1458992, and SES-1728853], U.S. Army Research Office [Grant MSN201957], and U.S. Air Force Office of Scientific Research [Grant FA9550-09-0538] is gratefully acknowledged. Keywords: sample path large deviations * evolutionary game theory * stochastic stability * Markov chains * potential games * congestion games, 1. Introduction Evolutionary game theory concerns the dynamics of aggregate behavior of populations of strategically interacting agents. To define these dynamics, one specifies the population size N, the game being [...]

By generalizing a recent result of Hong, Liu and Lai on characterizing the degree-sequences of simple strongly connected directed graphs, a characterization is provided for degree-sequences of simple k-node-connected digraphs. More generally, we solve the directed node-connectivity augmentation problem when the augmented digraph is degree-specified and simple. As for edge-connectivity augmentation, we solve the special case when the edge-connectivity is to be increased by one and the augmenting digraph must be simple. Funding: The research was supported by the Hungarian Scientific Research Fund--OTKA [Grant K109240]. The work of the first author was financed by a postdoctoral fellowship provided by the Hungarian Academy of Sciences. Keywords: degree-sequences * k-connected digraphs * connectivity augmentation, 1. Introduction There is an extensive literature of problems concerning degree sequences of graphs or digraphs with some prescribed properties such as simplicity or -connectivity. For example, Edmonds [8] characterized [...]

The main result of this paper is motivated by the following two apparently unrelated graph optimization problems: (A) As an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising k disjoint branchings [B.sub.i] each having a specified number [[mu].sub.i] of arcs. (B) As an extension of Ryser's maximum term rank formula, determine the largest possible matching number of simple bipartite graphs complying with degree-constraints. The solutions to these problems and to their generalizations will be obtained from a new min-max theorem on covering a supermodular function by a simple degree-constrained bipartite graph. A specific feature of the result is that its minimum cost extension is already NP-hard. Therefore classic polyhedral tools themselves definitely cannot be sufficient for solving the problem, even though they make some good service in our approach. Funding: The research was supported by the Hungarian Scientific Research Fund--OTKA [Grant K109240]. The work of the first author was financed by a postdoctoral fellowship provided by the Hungarian Academy of Sciences. Keywords: supermodular arc-covering * packing branchings * term rank, 1. Introduction Network flow theory provides a basic tool to conveniently treat various graph characterization and optimization problems such as the degree-constrained subgraph problem in a bipartite graph (or bigraph, [...]

The multiple exchange property for matroid bases is generalized for valuated matroids and M-natural concave set functions. The proof is based on the Fenchel-type duality theorem in discrete convex analysis. The present result has an implication in economics: The strong no complementarities condition of Gul and Stacchetti is, in fact, equivalent to the gross substitutes condition of Kelso and Crawford. Funding: This work was supported by The Mitsubishi Foundation, JST CREST [Grant JPMJCR14D2], and JSPS KAKENHI [Grant 26280004]. Keywords: discrete convex analysis * matroid * exchange property * combinatorial optimization, 1. Introduction Discrete convex analysis (Fujishige [5], Murota [17]) offers a general framework of discrete optimization, combining the ideas from submodular/matroid theory and convex analysis. It has found applications in [...]

Ryser's max term rank formula with graph theoretic terminology is equivalent to a characterization of degree sequences of simple bipartite graphs with a specific matching number. In a previous paper by the authors, a generalization was developed for the case when the degrees are constrained by upper and lower bounds. Here, two other extensions of Ryser's theorem are discussed. The first one is a matroidal model, while the second one settles the augmentation version. In fact, the two directions shall be integrated into one single framework. Funding: The research was supported by the Hungarian Scientific Research Fund-OTKA [Grant K109240]. The work of the first author was financed by a postdoctoral fellowship provided by the Hungarian Academy of Sciences. Keywords: matroids * term rank * bipartite matching * augmentation, 1. Introduction Ryser [13] derived a formula for the maximum term rank of a (0, l)-matrix with specified row sums and column sums. In graph theoretic terms, his theorem is [...]

We introduce an iterative method for solving linearly constrained optimization problems, whose nonsmooth nonconvex objective function is defined as the pointwise maximum of finitely many concave functions. Such problems often arise from reformulations of certain constraint structures (e.g., binary constraints, finite max-min constraints) in diverse areas of optimization. We state a local optimization strategy, which exploits piecewise-concavity of the objective function, giving rise to a linearized model corrected by a proximity term. In addition we introduce an approximate line-search strategy, based on a curvilinear model, which, similarly to bundle methods, can return either a satisfactory descent or a null-step declaration. Termination at a point satisfying an approximate stationarity condition is proved. We embed the local minimization algorithm into a Variable Neighborhood Search scheme and a Coordinate Direction Search heuristic, whose aim is to improve the current estimate of the global minimizer by exploring different parts of the feasible region. We finally provide computational results obtained on two sets of small- to large-size test problems. Keywords: nonsmooth optimization * minmax problems * nonconvex optimization * piecewise-concave, 1. Introduction We consider the following nonconvex nonsmooth optimization problem [mathematical expression not reproducible] (1) where [mathematical expression not reproducible] and we assume that * the component functions [f.sub.i](*), i[member [...]

We introduce concepts of metric regularity and metric subregularity of a positive-order for an implicit multifunction and provide new sufficient conditions for the implicit multifunctions to achieve the addressed properties. [...]

This work is concerned with finite-state irreducible Markov decision chains satisfying continuity-compactness requirements. It is supposed that the system is driven by a decision maker with utility function U, which, [...]

This work is devoted to extend several asymptotic results concerning repeated games with incomplete information on one side. The model we consider is a generalization of the classical model of [...]

In this work we construct subdivision schemes refining general subsets of [R.sup.n] and study their applications to the approximation of set-valued functions. Differently from previous works on set-valued approximation, our methods are developed and analyzed in the metric space of Lebesgue measurable sets endowed with the symmetric difference metric. The construction of the set-valued subdivision schemes is based on a new weighted average of two sets, which is defined for positive weights (corresponding to interpolation) and also when one weight is negative (corresponding to extrapolation). Using the new average with positive weights, we adapt to sets spline subdivision schemes computed by the Lane-Riesenfeld algorithm, which requires only averages of pairs of numbers. The averages of numbers are then replaced by the new averages of pairs of sets. Among other features of the resulting set-valued subdivision schemes, we prove their monotonicity preservation property. Using the new weighted average of sets with both positive and negative weights, we adapt to sets the 4-point interpolatory subdivision scheme. Finally, we discuss the extension of the results obtained in metric spaces of sets, to general metric spaces endowed with an averaging operation satisfying certain properties. Keywords Subdivision * Set-valued functions * Approximation * Symmetric difference metric Mathematics Subject Classification 26E25 * 41A65 * 68U99, 1 Introduction Approximation of set-valued functions (SVFs) has various potential applications in optimization, control theory, mathematical economics, medical imaging and more. The problem is closely related to the approximation of [...]

Probability discounting occurs when the subjective value of an outcome changes because its delivery is uncertain. The present study measured the reliability of rates of probability discounting. Participants completed a probability-discounting task that involved seven different outcomes. Some participants completed the task using the fill-in-the-blank (FITB) method and others using the multiple-choice (MC) method. Participants completed the task a second time either 4 or 12 weeks later. Data were analyzed using hyperbolic and hyperbolic-like functions, and by calculating the area under the discounting curve. The FITB method consistently produced steeper rates of discounting than the MC method. Discounting rates were generally reliable when discounting was analyzed using a hyperbolic function or area under the curve, but not when a hyperbolic-like function was used. Overall, reliability measures were somewhat lower than previously observed for delay discounting. These results suggest that rates of probability discounting are temporally reliable, but that the observed rates of discounting will depend on the type of method used to collect and analyze the discounting data. Key words: probability discounting, reliability, fill-in-the-blank method, multiple-choice method, university students, Discounting occurs when the subjective value of an outcome is altered because its delivery is delayed or uncertain (see Madden & Bickel, 2010, for a review). For instance, if you [...]

We discuss consistency of vanishingly smooth fictitious play, a strategy in the context of game theory, which can be regarded as a smooth fictitious play procedure, where the smoothing parameter [...]

Continuous nonnegative functions, such as Poisson rate functions, are sometimes approximated as piecewise-constant functions. We consider the problem of automatically smoothing such functions while maintaining the integral of each piece [...]

Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose various structural conditions on the clustering schemes, under the general heading of functoriality. Functoriality refers to the idea that one should be able to compare the results of clustering algorithms as one varies the dataset, for example by adding points or by applying functions to it. We show that, within this framework, one can prove a theorem analogous to one of Kleinberg (Becker et al. (eds.), NIPS, pp. 446-453, MIT Press, Cambridge, 2002), in which, for example, one obtains an existence and uniqueness theorem instead of a nonexistence result. We obtain a full classification of all clustering schemes satisfying a condition we refer to as excisiveness. The classification can be changed by varying the notion of maps of finite metric spaces. The conditions occur naturally when one considers clustering as the statistical version of the geometric notion of connected components. By varying the degree of functoriality that one requires from the schemes, it is possible to construct richer families of clustering schemes that exhibit sensitivity to density. Keywords Clustering * Functoriality * Chaining effect * Single linkage * Data analysis Mathematics Subject Classification Primary 62H30 * Secondary 68T10, 1 Introduction Clustering techniques play a very central role in various parts of data analysis. They can give important clues to the structure of datasets, and therefore suggest results and [...]

In four cases it is already known that the product of two distinct Jacobian theta functions having the same variable z and the same nome q is a multiple of [...]

Probability and time are integral dimensions of virtually any decision. To treat them together, we consider the prospect of receiving outcome x with a probability p at time t. We define risk and time distance, and show that if these two distances are traded off linearly, then preferences are characterized by three functions: a value function, a probability discount rate function, and a psychological distance function. The concavity of the psychological distance function explains the common ratio and common difference effects. A decreasing probability discount rate accounts for the magnitude effect. The discount rate and the risk premium depend on the shape of these three functions. Key words: risk preferences; time preferences; probability discount rate; subendurance; magnitude effect; psychological distance History: Received July 14, 2009; accepted July 19, 2011, by Peter Wakker, decision analysis. Published online in Article in Advance December 2, 2011., 1. Introduction Time and probability are fundamental attributes of virtually any decision. Decisions involving future risky consequences can be found in domains such as investment, saving, consumption, environmental preservation, and [...]

Approximate analytical solutions of the spin-zero version of the Duffin-Kemmer- Petiau (DKP) equation are obtained via an elegant ansatz after successive transformations for the ground state. As the DKP equation under a scalar term appears as a differential equation that is more complicated than that of the Klein-Gordon equation, the solutions might open new insights to the corresponding physics. PACS Nos: 03.65.Ca, 03.65.Pm, 03.65.Nk Nous obtenons des solutions analytiques approximatives de la version spin zero (scalaire) de l'equation de Duffin-Kemmer-Petiau, (DPK) via un ansatz elegant suivant des transformations successives pour le fondamental. Comme l'equation de DPK pour un scalaire apparait comme une equation differentielle qui est plus compliquee que l' equation de Klein-Gordon, les solutions pourraient fournir de nouveaux indices applicables a la physique correspondante. [Traduit par la Redaction], 1. Introduction The works of Duffin, Kemmer, and Petiau in 1930s introduced a basis that enabled physicists to investigate both spins zero and one particles on the basis of a [...]

In this work, we determine the conditions for the extremum of the figure of merit, [[theta].sup.2], in a degenerate semiconductor for thermoelectric (TE) applications. We study the variation of the function [[theta].sup.2] with respect to the reduced chemical potential [[mu].sup.*] using relations involving polylogarithms of both integral and nonintegral orders. We present the relevant equations for the thermopower, thermal, and electrical conductivities that result in optimizing [[theta].sup.2] and obtaining the extremum equations. We discuss the different cases that arise for various values of r, which depends on the type of carrier scattering mechanism present in the semiconductor. We also present the important extremum conditions for [[theta].sup.2] obtained by extremizing the TE power factor and the thermal conductivity separately. In this case, simple functional equations, which lead to solutions in terms of the Lambert W function, result. We also present some solutions for the zeros of the polylogarithms. Our analysis allows for the possibility of considering the reduced chemical potential and the index r of the polylogarithm as complex variables. PACS Nos: 05.30.-d, 72.20.Pa, 02.30.Gp Nous determinons ici les conditions d'extremisation de la figure de merite [[theta].sup.2] dans un semi-conducteur degenere en vue d'applications thermoelectriques (TE). Nous etudions la variation de la fonction [[theta].sup.2] en termes du potentiel chimique reduit [[mu].sup.*], en utilizant des relations impliquant des polylogarithmes d'ordre entier et non entier. Nous presentons les equations pertinentes pour la puissance thermique et les conductivites thermique et electrique qui resultent de l'optimization de [[theta].sup.2] et de l'obtention des equations d'extremisation. Nous analysons les cas correspondant aux differentes valeurs du parametre r qui depend du type du mecanisme de diffusion des porteurs dans le semi-conducteur. Nous presentons aussi les importantes conditions d'extremisation pour [[theta].sup.2] obtenues par extremisation separee du facteur de puissance TE et de la conductivite thermique. Dans ce cas, il en resulte de simples equations fonctionnelles, qui menent a des solutions en termes de la fonction W de Lambert. Nous presentons egalement des solutions pour les zeros des polylogarithmes. Notre analyse permet de tenir compte de la reduction possible du potentiel chimique et du parametre r du polylogarithme comme variables complexes. [Traduit par la Redaction], 1. Introduction There is considerable current interest in quasizerodimension physics that refers to the study of electrons and excitons in nanostructures. A polylogarithmic formulation of the statistical mechanics of ideal [...]

In this paper, the radius of convergence of the spheroidal power series associated with the eigenvalue is calculated without using the branch point approach. Studying the properties of the power series using the recursion relations among its coefficients in the new method offers some insights into the spheroidal power series and its associated eigenfunction. This study also used the least squares method to accurately compute the convergence radii to five or six significant digits. Within the circle of convergence in the complex plane of the parameter c = kF, where k is the wavenumber and F is the semifocal length of the spheroidal system, the extremely fast convergent spheroidal power series are computed with full precision. In addition, a formula for the magnitude of the upper bound of the error is obtained. PACS Nos: 02.30.Gp, 02.70.-c, 01.55.+b, 02.30.Hq, 02.60.Lz Nous calculons ici le rayon de convergence de la serie de puissance spheroidale associee aux valeurs propres sans utiliser l'approche du point de branchement. L'etude des proprietes des series de puissance par methode recursive entre les coefficients est une approche qui offre une nouvelle perception des series de puissance spheroidales et des fonctions propres associees. Nous utilisons la methode des moindres carres pour calculer de facon precise les rayons de convergence a cinq ou six chiffres significatifs. Les series de puissance a convergence extremement rapide sont calculees avec une complete precision a l'interieur du rayon de convergence dans le plan complexe du parametre c = kF,ou k est le nombre d'onde et F la demi-longueur focale du systeme spheroidal. Nous obtenons aussi une formule donnant la limite d'erreur superieure du calcul. [Traduit par la Redaction], 1. Introduction The calculation of spheroidal eigenvalues is an interesting subject in the literature. In the asymptotic regime in which the parameter c = kF (k, operating wavenumber; F, semifocal [...]

Artificial neural networks (ANNs) have been applied to heavy ion collisions. In the present work, the possibility of using ANN methods for modeling the multiplicity distributions, P([n.sub.s]), of shower particles produced from p, d, [sup.4]He, [sup.6]Li, [sup.7]Li, [sup.12]C, [sup.16]O, and [sup.24]Mg interactions with light (CNO) as well as heavy (AgBr) emulsions at 4.5 A GeV/c was investigated. Two different ANN approaches, namely radial basis function neural network (RBFNN) and generalized regression neural network (GRNN), were employed to obtain a mathematical formula describing these collisions. The results from RBFNN and GRNN models showed good agreement with the experimental data. GRNN models have a better performance than the RBFNN models. This study showed that the RBFNN and GRNN models are capable of accurately predicting the P([n.sub.s])of shower particles in the training and testing phases. PACS Nos: 11.80.-m, 13.85.-t, 07.05.Mh, 82.20.wt Nous avons analyse des collisions d'ions lourd a l'aide d'une methode de reseau de neurones artificiels (ANN). Nous utilisons ici le ANN pour modeliser les distributions de multiplicite P([n.sub.s]) des gerbes de particules produites par des p, d, [sup.4]He, [sup.6]Li, [sup.12]C, [sup.16]O et [sup.24]Mg sur des emulsions legeres (CNO) et lourdes (AgBr) a 4,5 A GeV/c. Deux approches neuronales differentes ont ete utilisees, le reseau de neurones a fonction de base radiale (RBFNN) et le reseau de neurones a regression generalisee (GRNN), afin d'obtenir une formule mathematique pour decrire ces collisions. Les resultats de RBFNN et de GRNN sont en bon accord avec les donnees experimentales. Les modeles GRNN performent mieux que les modeles RBFNN. Cette etude montre que les modeles GRNN et RBFNN sont capables de predire de facon precise les P([n.sub.s]) pendant les phases d'apprentissage et de test. [Traduit par la Redaction], 1. Introduction The analysis of heavy ion collisions at high energies is an important field of particle and nuclear physics. The number of particles produced in an interaction, called the [...]

Theoretical studies of electronic configurations of several lanthanide ions in the Racah-Slater approach were performed with the standard suite of codes by R.D. Cowan, including a fitting of energy parameters. Configuration interaction was considered explicitly in the low configurations and was processed by effective parameters for doubly-excited far configurations. Mean errors lower than 100 [cm.sup.-1] were obtained. Systematic differences are noticed between radial integrals calculated by ab initio PHFR and the [P.sub.fit] fitted values. The consistency of the scaling factors SF(P) = [P.sub.fit]/[P.sub.HFR] and of the effective parameters for far configuration effects is shown. In an application to Tm II, the predicted transition probabilities compared well with line intensities and led to the finding of new energy levels. In Nd II, the configuration 4f5 is identified. PACS Nos: 31.15.Md, 32.30.Jc, 32.70.Cs, 42.55.Rz, 52.80.Yr On etudie des configurations electroniques d'ions de lanthanides par la methode de Racah-Slater au moyen des programmes de R.D. Cowan. Le traitement de l'interaction de configurations par extension de la base de configurations et par des parametres effectifs autorises dans la version standard du code Cowan permettent d'aboutir a des erreurs moyennes inferieures a 100 [cm.sup.-1]. Les facteurs d'echelle SF(P) = [P.sub.fit]/PHFR liant le parametre ajuste a l'integrale radiale a priori sont faiblement dependants de l'element et du degre d'ionisation. Des resultats recents sont commentes et une comparaison des intensites de raies non classees avec les probabilites de transition calculees conduit a ameliorer l'interpretation de Tm II. Quant a Nd II, la configuration 4f5 est maintenant identifiee. [Traduit par la Redaction], 1. Introduction The modelling of astrophysical and controlled fusion plasmas has been an incentive for many theoretical studies of neutral and weakly charged ions of lanthanides and 5d elements in [...]

This paper presents a predictive model for compressive creep behavior of high-density polyethylene (HDPE) commonly used to manufacture polymeric piling and geosynthetics. Accelerated methods to predict the tensile creep of polymers are already available. In this paper, a method to predict the compressive creep of viscoelastic polymers is proposed based on the equivalence of strain energy density (SED) between conventional constant-stress creep tests and strain-controlled stress-strain (ramp loading at different constant strain rates) tests. There is good agreement between the creep behaviors obtained from conventional tests and SED predictions when two stress-strain experiments with strain rates differing by two or more orders of magnitude are used. SED was also used as a basis for predicting the onset of tertiary creep. Finally, onset of tertiary creep was used for rational selection of the ultimate strength of viscoelastic materials, whose strength is inversely proportional to duration of loading. DOI: 10.1061/(ASCE)MT.1943-5533.0000136 CE Database subject headings: Creep; Polymer; Polyethylene; Piles; Viscoelasticity: Compressive strength. Author keywords: Creep; Polymer; High-density polyethylene; HDPE; Pile; Viscoelastic; Strength, compression; Monotonic; Modulus; FRP, fiber-reinforced polymer; Compression; Thermoplastic; Strength; Ultimate stress.

We study the problem of a nonrelativistic quantum particle moving on a real line with an idealized and localized singular interaction with zero range at x = 0 (i.e., a point interaction there). This kind of system can be described in two ways: (i) by considering an alternative free system (i.e., without the singular potential) but excluding the point x = 0 (In this case, the point interaction is exclusively encoded in the boundary conditions.) and (ii) by explicitly considering the singular interaction by means of a local singular potential. In this paper we relate, compare, and discuss, in a simple and pedagogical way these two equivalent approaches. Our main goal in this paper is to introduce the essential ideas about point interactions in a very accesible form to advanced undergraduates. PACS Nos: 03.65.-w, 03.65.Db, 03.65.Ge Nous etudions le probleme d'une particule quantique non relativiste sur la ligne reelle avec une interaction de portee nulle singuliere, idealisee et localisee a x = 0 (c.-a-d., une interaction ponctuelle en ce point). On peut deecrire ce type de systeme de deux facons. (i) On peut etudier le systeme alternatif libre en excluant le point x = 0 (sans le potentiel singulier), auquel cas, le point d'interaction est exclusivement encode dans la condition limite. (ii) On peut considerer l'interaction singuliere comme etant un potentiel local singulier. Nous analysons, relions et comparons ici ces deux approches equivalentes de facon pedagogique simple. Notre objectif est de presenter de facon accessible les points essentiels de ce problemes aux etudiants en fin de premier cycle. [Traduit par la Redaction], 1. Introduction Many aspects of point interactions (sharply localized singular perturbations or simply called contact interactions) such as the common Dirac delta function (or rather distribution), are fascinating, such as [...]

In this paper we discuss the influence of two different sets of weighting functions on the accuracy behavior of T-matrix calculations for scalar scattering problems. The first set of weighting functions is related to one of Waterman's original approaches. The other set results into a least-squares scheme for the transmission problem. It is shown that both sets of weighting functions produce results with a converse accuracy behavior in the near and far fields. Additional information, such as reciprocity and the fulfillment of the boundary condition, are needed to choose the set of weighting functions that is most appropriate for a certain application. The obtained criteria are applied afterward to an iterative T-matrix approach we developed to analyze scattering on regular particle geometries with an impressed but slight surface irregularity. However, its usefulness is demonstrated in this paper by analyzing the far-field scattering behavior of Chebyshev particles of higher orders. OCIS codes: 290.0290, 290.5825, 000.4430.

By expressing a scaled Zernike radial polynomial as a linear combination of the unscaled radial polynomials, we give a simple derivation for determining the Zernike coefficients of an aberration function of a scaled pupil in terms of their values for a corresponding unscaled pupil. OCIS codes: 110.0110, 120.0120, 010.7350, 220.1010, 120.3180, 220.0220.

Geometrically nonlinear vibrations of circular plate with two cut-outs are simulated by the yon Karman equations with respect to displacements. The combination of the Rayleigh-Ritz method and the R-function method, which allows satisfying all boundary conditions, is applied to obtain the vibration modes of the plate. The nonlinear vibrations are expanded using these vibrations modes. The dynamical system with three degrees of freedom is derived by Galerkin method. The influence of cut-outs size on linear and nonlinear vibrations of the plate is analyzed. For different parameters of cut-outs, different internal resonances occur in the plate. The nonlinear vibrations of the system for different internal resonances are analyzed by multiple scale method. [DOI: 10.1115/1.4001496] Keywords: circular plates with cut-outs, R-function method, conjugate modes, multiple scale method, internal resonances

The continued fractions for special functions package (in the sequel abbreviated as CFSF package) complements a systematic study of continued fraction representations for special functions. It provides all the functionality to create continued fractions, in particular k-periodic or limit k-periodic fractions, to compute approximants, make use of continued fraction tails, perform equivalence transformations and contractions, and much more. The package, developed in Maple, includes a library of more than 200 representations of special functions, of which only 10% can be found in the 1964 NBS Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables by M. Abramowitz and I. Stegun. Categories and Subject Descriptors: G.1.2 [Numerical Analysis]: Approximation--Special function approximations General Terms: Algorithms, Documentation Additional Key Words and Phrases: CAS software, continued fractions, Maple, special functions DOI = 10.1145/1527286.1527289

The interslice force function f(x) is a major assumption of the limit equilibrium method, which is important but has not been adequately considered in the past. In this paper, f(x) is taken as the control variable, and the upper and lower limits of the factor of safety for a general slope will be determined by a global optimization analysis. Based on this approach, f(x) will be determined and investigated. We demonstrate that f(x) cannot be arbitrarily assigned if a set of acceptable internal forces is required. The present approach can be presented practically as a lower bound approach with the advantage that failure to converge is virtually eliminated, which is not possible with all other existing 'rigorous' methods. The 'present proposal' attempts to answer several important questions in the basic theory of slope stability analysis, and provides a f(x) based on the lower bound approach statically admissible forces throughout the whole failure zone. Currently, different assumptions will give different factors of safety to the same problem, and this situation will be overcome by the use of the present proposal. The present proposal is also proven to give a result equal to the slip line solution for a simple footing on clay which is not possible for other classical slope stability methods, which has demonstrated that the applicability of the 'present proposal' for general difficult problems. DOI: 10.1061/(ASCE)GT.1943-5606.0000317 CE Database subject headings: Slope stability; Safety; Convergence; Limit equilibrium. Author keywords- Slope stability analysis; Factor of safety; Interslice force function; Global maximum; Lower bound theorem; Convergence.

Let A be the class of analytic functions in the unit disk that are normalized with f(0) = f'(0) - 1 = 0. In this paper we study the class [G.sub.[lambda]] = {f [member of] A: [absolute value of 1 + zf'(z)/f'(z)/zf'(z)/f(z) - 1] < [lambda], z [member of] u}, and give sharp sufficient conditions that embed it into the class [S.sup.*][A, B, b] = {f [member of] A: 1 + 1/b (zf'(z)/f(z) - 1) [??] 1 + Az/1 + Bz}, where -1 [less than or equal to] B < A [less than or equal to] 1, b [not equal to] 0 and ' [??] ' denotes the usual subordination. Keywords Univalent function, starlike function, criteria, Jack lemma., [section]1. Introduction and preliminaries Let A be the class of functions f(z) that are analytic in the unit disk U = {z : [absolute value of z] < 1} and [...]

In this article we prove the Smarandache-Patrascu's theorem in relation to the inscribed orthohomological triangles using the barycentric coordinates. Keywords Smarandache-Patrascu's theorem, barycentric coordinates., Definition. Two triangles and ABC and [A.sub.1][B.sub.1][C.sub.1], where [A.sub.1] ∈ BC, [B.sub.1] ∈ AC, [C.sub.1] ∈ AB, are called inscribed ortho homological triangles if the perpendiculars in [A.sub.1], [B.sub.1], [C.sub.1] [...]

The triangle T(a, b, c) with angles a, b, c, and the triangle T(a', b', c') with angles a', b', c' are said to be pseudo Smarandache related if Z(a) =Z(a'), Z(b) =Z(b'), Z(c) =Z(c'), and the pair of triangles T(a, b, c) and T(a', b', c') are said to be Smarandache related if S(a) = S(a'), S(b) = S(b'),S(c) = S(c'), where Z(*) is the pseudo Smarandache function, and S(.) is the Smarandache function. This paper lists all the dissimilar pseudo Smarandache related triangles, under the additional condition that a =a', found by computer search. Keywords Pseudo Smarandache function, Smarandache function, pseudo Smarandache related triangles, Smarandache function related triangles., §1. Introduction The pseudo Smarandache function, denoted by Z(n), has been introduced by Kashihara [1]. Since then, the pseudo Smarandache function has seen several generalizations in different directions. One such [...]

We present a constraint analysis methodology for linear matrix inequality constraints. If the constraint set is found to be feasible, we search for a minimal representation; otherwise, we search for [...]

We propose a new heuristic for nonlinear global optimization combining a variable neighborhood search framework with a modified trust-region algorithm as local search. The proposed method presents the capability to [...]

We examine symbolic tools associated with two modeling systems for mathematical programming, which can be used to automatically detect the presence or absence of convexity and concavity in the objective [...]

We propose a new robust optimization method for problems with objective functions that may be computed via numerical simulations and Incorporate constraints that need to be feasible under perturbations. The [...]

In this paper, some complete monotonicity properties of functions related to the gamma function and Barnes G-function are proved. Keywords Gamma function, double gamma function, Barnes G-function, complete monotonicity, asymptotic expansion., [section] 1. Introduction A function f is said to be completely monotonic over (a, b), where -[infinity] [less than or equal to] a < b [less than or equal to] [...]

For any positive integer n, the Pseudo-Smarandache function Z(n) is defined as Z(n) = min {m : m [member of] N, n | m (m+1)/2}. And the F. Smarandache function SL(n) is defined as the smallest positive integer k such that n [absolute value of [1, 2, ..., k]], where [1, 2, ..., k] denotes the least common multiple of 1, 2, ..., k. In this paper, we use the elementary methods and congruences to study the solvability of the equation Z(n) + SL(n) = n, and give its all positive integer solutions. Keywords Pseudo-Smarandache function, F. Smarandache LCM function, equation, solution, congruences., [section] 1. Introduction and results For any positive integer n [greater than or equal to] 1, the Pseudo-Smarandache function Z(n) is defined as the smallest positive integer m such that [...]

The main aim of the following text is to study the semigroup of continuous functions from a topological space to itself under the operation of composition of maps, in the point of view of Smarandache semigroup's approach. Keywords Continuous map, Smarandache semigroup, topological space., [section] 1. Introduction As it has been mentioned [3, page 29], a Smarandache semigroup S is a semigroup which is not a group and has a proper subset A with [...]

An integer a is called regular (mod n) if there is an integer x such that [a.sup.2]x [equivalent to] a(mod n). Let [??](n) denote the number of regular integers a(mod n) such that 1 [less than or equal to] a [less than or equal to] n, [phi](n) is the Euler function. In this paper we investigate the mean value of the function [([??](n)/[phi](n)).sup.r], where r [greater than or equal to] 1 is a fixed integer. Keywords Regular integers (mod n), Euler's function, average order, convolution method, Euler product., [section] 1. Introduction Let n > 1 be an integer. Consider the integers a for which there exists an integer x such that [a.sup.2]x = a(mod n). Properties of these [...]

Orthogonal polynomials play a very important role in analysis, mainly because functions belonging to very general classes can be expanded in series of orthogonal polynomials. The main purpose of this paper is using the elementary method and the properties of power series to study the calculating problem of one kind summation involving the Laguerre polynomials, and give some interesting identities. Keywords Laguerre polynomials, power series, generating function, elementary method, orthogonal polynomials, identity., [section] 1. Introduction For any real number x, the famous Laguerre polynomials [L.sub.n](x) are defined by the coefficients of the power series expansion of the function 1/1-t [e.sup.-xt/1-t]. That is, [...]

For any positive integer n, the Smarandache dual function S** (n) is defined as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] The main purpose of this paper is using the elementary methods to study the convergent properties of an infinity series involving S**(n), and give an interesting limit formula for it. Keywords The Smarandache dual function, limit problem, elementary method., [sections]1. Introduction and Results For any positive integer n, the Smarandache dual function S**(n) is defined as the greatest positive integer 2m - 1 such that (2m - 1)1! divide [...]

Let T(n) denote the product of divisors of the positive integer n. We introduce and study some basic properties involving two functions, which are the minimum, resp. the maximum of certain integers connected with the divisors of T(n). Keywords Arithmetic functions, product of divisors of an integer., 1. Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denote the product of all divisors of n. The product-of- divisors minimum, resp. maximum functions will be defined by T(n) = min{k [...]

Using the exact Airy function formalism and the transfer-matrix technique, we have numerically investigated the effect of structural and topological correlated disorder, introduced by triplet, on the miniband structure of the GaAs/[Al.sub.x][Ga.sub.1-x]-As superlattices. These systems exhibit a miniband of extended states, around a critical energy, lying to the typical structure of the trimer cell. The states close to this resonant energy consist of weakly localized states, while in band tails i.e., for negligible transmission, the states are strongly localized. This is evidence of the suppression of localization in the RTB superlattices. The extended states due to the basic cell (triple barrier) remain for correlated structural and topological disorder. However, the commuting extended state exists only in the correlated structural disorder, where the periodicity of the system is preserved. Commuting resonance energy is theoretically demonstrated in this paper, and the obtained values are in good agreement with the existing numerical results. PACS Nos: 73.20.At, 73.21.Ac, 73.21.Cd, 85.30.Vw Utilisant le formalisme exact de la fonction d'Airy et la technique de la matrice de transfert, nous avons analyse numeriquement l'effet du desordre structurel et topologiquement correle, induit par un etat triplet sur la structure minibande des superreseaux GaAs/[Al.sub.x][Ga.sub.1-x]-As. Ces systemes possedent une minibande d'etats etendus, autour d'une energie critique, proche de la structure typique de la cellule trimere. Les etats pres de cette energie de resonance sont des etats faiblement localises, alors que dans les queux de bande, donc pour des transmissions negligeables, les etats sont tres localises. Ceci demontre la suppression de la localisation dans les superreseaux RTB. Les etats etendus sont dus a la cellule de base (barriere triple), toujours pour le desordre correle, qu'il soit structurel ou topologique. Cependant, l'etat etendu commutant existe seulement dans le desordre correle structurel ou la periodicite du systeme est preservee. Nous demontrons ici l'existence de l'energie de resonance commutante. Les valeursobtenues sont en bon accord avec les resultats numeriques existants. [Traduit par la Redaction], 1. Introduction The GaAs/[Al.sub.x][Ga.sub.1-x]-As semiconductor superlattices provide a good basis for many established commercial and new technological applications in electronic and optoelectronic devices, such as photo detectors [1], avalanche photo [...]

Let n be any positive integer, [P.sub.d](n) denotes the product of all positive divisors of n. The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of a new arithmetical function S ([P.sub.d](n)), and give an interesting asymptotic formula for it. Keywords Smarandach function, Divisor product sequences, Composite function, mean value, Asymptotic formula., [section]1. Introduction For any positive integer n, the famous F.Smarandache function S(n) is defined as the smallest positive integer m such that n divide m!. That is, S(n) = min{m [...]

In this paper, we mainly discuss the Smarandache relation on U-semiabundant semigroups. Keywords U-semiabundant semigroups, Green relations, Natural partial orders., [section]1. Introduction In generalizing regular semigroups, a generalized Green relation [L.sup.U] was introduced by M. V. Lawson [6] on a semigroup S as follows: Let E be the set of [...]

Abstract In this note, we will introduced Smarandache Mukti-Squares which are non-associative structures. Arun S. Muktibodh in [2] has defined and studied Smarandache Mukti-Squares (SMS) and gave some open problems. We will extend some SMS to Latin squares that satisfies in problems propounded by Muktibodh [2]. Keywords Quasigroups, Smarandache quasigroups, latin square, non-associative structure, [section] 1. Introduction Smarandache theory is one of the new branches in mathematics that were first defined and studied by Prof. F. Smarandache and W. B. Kandasamy. Study of algebraic [...]